Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-3y &= -3 \\ 5x-8y &= -8\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = -5x-8$ Divide both sides by $-8$ to isolate $y$ $y = {\dfrac{5}{8}x + 1}$ Substitute this expression for $y$ in the first equation. $2x-3({\dfrac{5}{8}x + 1}) = -3$ $2x - \dfrac{15}{8}x - 3 = -3$ Simplify by combining terms, then solve for $x$ $\dfrac{1}{8}x - 3 = -3$ $\dfrac{1}{8}x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $2( 0)-3y = -3$ $-3y = -3$ $-3y = -3$ $y = 1$ The solution is $\enspace x = 0, \enspace y = 1$.